![]() ![]() ![]() The probability of randomly selecting a score between -1.96 and +1.96 standard deviations from the mean is 95% (see Fig. Proportion of a standard normal distribution (SND) in percentages. For example, there is a 68% probability of randomly selecting a score between -1 and +1 standard deviations from the mean (see Fig. The SND allows researchers to calculate the probability of randomly obtaining a score from the distribution (i.e. Therefore, one standard deviation of the raw score (whatever raw value this is) converts into 1 z-score unit. The standard deviation of any SND always = 1.For example, if the distribution of raw scores if normally distributed, so is the distribution of z-scores. z-distribution) is always the same shape as the raw score distribution.
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